What is the general solution for solvefor y,x=3sin(y) ?

The general solution for solvefor y,x=3sin(y) is y=arcsin(x/3)+2pin,y=pi+arcsin(-x/3)+2pin

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solvefor y,x=3sin(y)

solve for

y, x = 3 sin (y)

y = arcsin (\frac{x}{3}) + 2 πn, y = π + arcsin (- \frac{x}{3}) + 2 πn

Solution steps

x = 3 sin (y)

Switch sides

3 sin (y) = x

Divide both sides by

3

3 sin (y) = x

Divide both sides by

3

\frac{3 sin ( y )}{3} = \frac{x}{3}

Simplify

sin (y) = \frac{x}{3}

sin (y) = \frac{x}{3}

Apply trig inverse properties

sin (y) = \frac{x}{3}

General solutions for

sin (y) = \frac{x}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

y = arcsin (\frac{x}{3}) + 2 πn, y = π + arcsin (- \frac{x}{3}) + 2 πn

y = arcsin (\frac{x}{3}) + 2 πn, y = π + arcsin (- \frac{x}{3}) + 2 πn

\frac{tan ( θ )}{cot ( θ )} = 1

4 sin^{2} (x) = 4

tan (x) = \frac{- \frac{4}{3} 3}{- 4}

3 - 2 sin (θ) = - 3 + 2 sin (θ)

sin (x) - 0.75 = 0

What is the general solution for solvefor y,x=3sin(y) ?
The general solution for solvefor y,x=3sin(y) is y=arcsin(x/3)+2pin,y=pi+arcsin(-x/3)+2pin